There's another good analogy if you are familiar with a collegiate university like Oxbridge, Durham or London. The individual colleges (heya) are reponsible for recruiting students, seeing to their living needs and basic discipline, training them and then entering them for the examinations. The University (Kyokai) sets the standards, conducts the examinations (basho) and awards the qualifications. The numbers of people involved are hugely different, but the principles are much the same.
One difference is that these days Cambridge Colleges (at least, I don't know about The Other Place) hire professional staff to do a lot of the non-academic work. There's often a Fellow (Oyakata) nominally in charge of something but someone with outside experience doing the day to day work, although in some cases (eg the Bursar, effectively the business manager of the College) the person with outside experience is also appointed as a Fellow to give them the leverage and authority their job requires.